A note on polynomial maps having fibers of maximal dimension
| Autor: | Boulos El Hilany |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Polynomial (hyperelastic model)
Fiber (mathematics) General Mathematics Dimension (graph theory) Polytope Codimension Combinatorics Generic polynomial Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry FOS: Mathematics 12D10 14E05 52B11 Algebraic Geometry (math.AG) Finite set Mathematics |
| Zdroj: | Colloquium Mathematicum. 166:129-136 |
| ISSN: | 1730-6302 0010-1354 |
| DOI: | 10.4064/cm8162-8-2020 |
| Popis: | For any two integers $k,n$, $2\leq k\leq n$, let $f:(\mathbb{C}^*)^n\rightarrow\mathbb{C}^k$ be a generic polynomial map with given Newton polytopes. It is known that points, whose fiber under $f$ has codimension one, form a finite set $C_1(f)$ in $\mathbb{C}^k$. For maps $f$ above, we show that $C_1(f)$ is empty if $k\geq 3$, we classify all Newton polytopes contributing to $C_1(f)\neq \emptyset$ for $k=2$, and we compute $|C_1(f)|$. Comment: Final version, Minor corrections, 6 pages, to appear in Colloquium Mathematicum |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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